Learning temporal probabilistic causal models from longitudinal data

Medical problems often require the analysis and interpretation of large collections of longitudinal data in terms of a structural model of the underlying physiological behavior. A suitable way to deal with this problem is to identify a temporal causal model that may effectively explain the patterns observed in the data. Here we will concentrate on probabilistic models, that provide a convenient framework to represent and manage underspecified information; in particular, we will consider the class of Causal Probabilistic Networks (CPN). We propose a method to perform structural learning of CPNs representing time-series through model selection. Starting from a set of plausible causal structures and a collection of possibly incomplete longitudinal data, we apply a learning algorithm to extract from the data the conditional probabilities describing each model. The models are then ranked according to their performance in reconstructing the original time-series, using several scoring functions, based on one-step ahead predictions. In this paper we describe the proposed methodology through an example taken from the diabetes monitoring domain. The selection process is applied to a set of input-output models that generalize the class of ARX models, where the inputs are the insulin and meal intakes and the outputs are the blood glucose levels. Although the physiological process underlying this particular application is characterized by strong non-linearities and low data reliability, we show that it is possible to obtain meaningful results, in terms of conditional probability learning and model ranking power.